Among the linear measurements of the cranium, the one which serves to give the most exact index of volume is the maximum circumference.
This index, nevertheless, is not a perfect one, in the same sense that the stature, for instance, is a perfect index in respect to the body, because in the case of the cranium another element enters in: the form. The cranial circumference of an extremely brachycephalic cranium (almost circular) may contain a larger surface (and consequently include a larger volume), than a maximum circumference of the same identical measure, which belongs to an extremely dolichocephalic cranium (approaching the shape of an elongated ellipse). This may be easily understood if we imagine a loop of thread laid out in the form of a circle: if we pull it from two opposite sides, the enclosed area diminishes until it finally disappears as the two halves of the thread close together, while the length of the thread itself remains unaltered.
Nevertheless, the maximum circumference still remains the linear index best adapted to represent the volume; indeed, the authorities take its proportional relation to the stature as representing the reciprocal degree of development between head and body at the different successive ages.
Here are the figures which Daffner gives in this connection:
DEVELOPMENT OF THE STATURE AND OF THE CEPHALIC PERIMETER FROM BIRTH TO THE AGE OF ELEVEN YEARS
| Males | Females | ||||||
|---|---|---|---|---|---|---|---|
| Number of subjects | Age | Stature in centimetres | Cranial perimeter, centimetres | Number of subjects | Age | Stature in centimetres | Cranial perimeter, centimetres |
| 65 | At birth | 51.17 | 34.58 | 65 | At birth | 50.27 | 34.23 |
| 11 | 1.55 | 74.18 | 46.74 | 10 | 1.39 | 77.20 | 46.45 |
| 30 | 2.43 | 85.32 | 48.03 | 30 | 2.45 | 83.48 | 47.23 |
| 53 | 3.34 | 91.88 | 49.20 | 49 | 3.43 | 89.97 | 47.73 |
| 112 | 4.43 | 96.64 | 49.55 | 81 | 4.50 | 96.07 | 48.37 |
| 244 | 5.42 | 103.21 | 50.21 | 208 | 5.40 | 100.61 | 48.76 |
| 234 | 6.41 | 106.49 | 50.73 | 179 | 6.37 | 104.92 | 49.87 |
| 30 | 7.30 | 114.47 | 51.66 | 25 | 7.36 | 117.36 | 50.38 |
| 28 | 8.38 | 112.10 | 51.97 | 24 | 8.41 | 121.58 | 50.72 |
| 27 | 9.40 | 128.41 | 52.38 | 30 | 9.40 | 126.76 | 51.10 |
| 21 | 10.34 | 129.12 | 52.24 | 28 | 10.40 | 130.00 | 51.08 |
| 20 | 11.42 | 135.84 | 52.50 | 31 | 11.46 | 137.04 | 51.42 |
DEVELOPMENT OF THE STATURE AND OF THE CEPHALIC PERIMETER BETWEEN THE YEARS OF 13 AND 22
| Number of subjects | Age | Stature in centimetres | Cranial perimeter, centimetres |
|---|---|---|---|
| 13 | 13.39 | 147.92 | 52.83 |
| 24 | 14.50 | 149.21 | 53.53 |
| 20 | 15.38 | 163.55 | 54.34 |
| 41 | 16.43 | 162.53 | 53.34 |
| 35 | 17.36 | 167.93 | 55.89 |
| 26 | 18.35 | 171.65 | 54.91 |
| 15 | 19.40 | 172.97 | 55.48 |
| 6 | 20.05 | 173.97 | 56.50 |
| 342 | 21.02 | 168.08 | 55.37 |
| 171 | 22.22 | 168.08 | 55.62 |
One very important research made by Daffner is in reference to the maximums and minimums that are normal for each successive age. This is extremely useful for the purpose of diagnosing the morphological normality in relation to the age. He naturally bases his figures upon subjects studied by him personally, who altogether form an aggregate number of 2,230, and are not always sufficiently numerous when distributed according to their ages. Nevertheless, in the great majority of groups, especially those including the younger children, the number of subjects is sufficient and even superabundant.